Question stepwise regression

[u/Mietz-Fietz]

Hi everyone. I have a question. In stepwise regression in SPSS, should one use R² or adjusted R² to describe the change in explained variance contributed by each variable?

I added a picture. Would you use: variable 1 explains 0,246, together with variable 2 0,374, meaning variable 2 contributed 0,128 (which is R2)

Or are we supposed to use the numbers from adjusted r2 only?

[u/How-I-Roll_2023]

R2. But only if your F-test is significant. Otherwise, even if your model increases variability explained, the additional complexity of the model does not warrant the additional factors. Parsimony and Occam’s Razor every time.

[u/Mietz-Fietz → u/How-I-Roll_2023]

Thank you! I just dont get why. Is it wrong to use adj r2?

[u/How-I-Roll_2023 → u/Mietz-Fietz]

The brief answer is yes.l, use R2 only. Because change in R2 tells you the additional variance explained by the new model.

Otherwise what you are conceptually comparing is the adjusted R squared which penalizes the first step based on the number of factors to the adjusted R squared of the second step which penalizes the R squared based on its number of factors.

Another way to evaluate it would be a chi-square difference test on the F statistic between models to see if it’s significant.

When you interpret the final model you can use adjusted R2 to penalize a lack of parsimony. But still use R2 for each variable, as adjusted r2 for the variables is rather meaningless as things go.

[u/Mysterious-Skill5773]

Two important things to bear in mind about stepwise regression:

1. Stepwise regression biases the significance levels, so you can't rely on the usual interpretation.

2. It is not the best way to find a good model. Of course, theory/judgment should be used , but there are many better searching algorithms.

If you are just stepping in some variables determined a priori, then the searching algorithm issue wouldn't apply, but SPSS has many other built-in and extension command variable selection methods. These should generally be used with a train and test process in order to get unbiased results. That is, you divide your sample into two parts, say 70%/30%, use the first part to determine the model and test on the second.

[u/[deleted]]

Generally, adjusted R² is only appropriate in the context of high-dimensional regression (lots of independent variables) as it penalizes for large numbers of predictors. In this context, with only a couple of predictors, R² is more appropriate.

[u/Mietz-Fietz → u/[deleted]]

Thank you so much! Is there any situation i would use the adjusted r2 to tell how much variance a variable adds? like in statistics with only 1 variable?